A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 ho... A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Which method did you use for finding the mean, and why? Read more

Steps to Solve

1. Find the midpoint of each class interval

To calculate the mean from a frequency table with class intervals, we first need to find the midpoint of each interval. The midpoint is calculated as (lower limit + upper limit) / 2.

For the interval 0-2: $(0 + 2) / 2 = 1$ For the interval 2-4: $(2 + 4) / 2 = 3$ For the interval 4-6: $(4 + 6) / 2 = 5$ For the interval 6-8: $(6 + 8) / 2 = 7$ For the interval 8-10: $(8 + 10) / 2 = 9$ For the interval 10-12: $(10 + 12) / 2 = 11$ For the interval 12-14: $(12 + 14) / 2 = 13$

2. Multiply the midpoint by the frequency for each interval

Multiply each midpoint by the corresponding number of houses (frequency).

$1 \times 1 = 1$ $3 \times 2 = 6$ $5 \times 1 = 5$ $7 \times 5 = 35$ $9 \times 6 = 54$ $11 \times 2 = 22$ $13 \times 3 = 39$

3. Sum the products obtained in the previous step

Add all the products calculated in step 2.

$1 + 6 + 5 + 35 + 54 + 22 + 39 = 162$

4. Sum the frequencies

Add the number of houses (frequencies).

$1 + 2 + 1 + 5 + 6 + 2 + 3 = 20$

5. Calculate the mean

Divide the sum of the products (from step 3) by the sum of the frequencies (from step 4).

Mean = $\frac{162}{20} = 8.1$